Here are some pointers. With video framerates, the higher they are the smoother the footage appears to be. For example, films are shot at 24fps usually (fps = frames per second), and as a result look 'filmic'. Higher framerates like 50fps (PAL regions) and 60fps (NTSC regions) give video a smooth motion look. Sports and TV soap operas use these framerates, and they're good for filming families and holidays if your camera supports it (which yours does).
Regarding P and I... Never use i unless there's no other option. It's horrible. It stands for 'interlaced' and means that TWO frames are stored in one by having one line of pixels showing the first frame, and the second line of pixels showing the next frame, alternating all the way down the image. It's basically a leftover from analogue TV days, and can cause artifacts and problems when it comes to editing the clips unless you set up your editing software correctly.
P stands for 'progressive', and each frame is saved one after another as a sequence. Simple, more detailed, more efficient, and easier to edit with. All video you watch online is progressive.
So, I guess the best framerate option for your use is 60p.
If you're shooting to edit, always shoot a few seconds more after you think you've finished recording. It gives you some extra room to play with in the edit (such as fades).
When you're filming, make sure that you stick with your subject, rather than going here there and everywhere, unless it's something worth changing to. Treat them like photographs if it's a video of something stationary, but add some movement to keep things interesting, like a pan, but make sure it's relevant.
